What is 2xe^{x^2}(e^{-x^2}) ?

The solution to 2xe^{x^2}(e^{-x^2}) is 2x

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simplify 2xe^{x^2}(e^{-x^2})

simplify

2 x e^{x^{2}} (e^{- x^{2}})

2 x

Solution steps

2 x e^{x^{2}} (e^{- x^{2}})

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

e^{x^{2}} e^{- x^{2}} = e^{x^{2} - x^{2}}

= 2 x e^{x^{2} - x^{2}}

Add similar elements:

x^{2} - x^{2} = 0

= 2 x e^{0}

Apply rule

a^{0} = 1, a \neq = 0

e^{0} = 1

= 2 \cdot 1 \cdot x

Multiply the numbers:

2 \cdot 1 = 2

= 2 x

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